Arabian Journal of Mathematics

, Volume 6, Issue 2, pp 79–86 | Cite as

Approximation by rational functions in Smirnov classes with variable exponent

  • Ahmed Kinj
  • Mohammad Ali
  • Suliman Mahmoud
Open Access


In this article, we investigate the direct problem of approximation theory in the variable exponent Smirnov classes of analytic functions, defined on a doubly connected domain bounded by two Dini-smooth curves.

Mathematics Subject Classification

30E10 41A20 41A25 46E30 


  1. 1.
    Cruz-Uribe, D.V.; Fiorenza, A.: Variable lebesgue spaces foundation and harmonic analysis. Birkhäuser, Basel (2013)CrossRefMATHGoogle Scholar
  2. 2.
    Diening, L., Harjulehto, P., Hästö, P., Michael Ruzicka, M.: Lebesgue and Sobolev Spaces with Variable Exponents. Springer, Heidelberg, Dordrecht, London, New York (2011)Google Scholar
  3. 3.
    Goluzin, G.M.: Geometric theory of functions of a complexvariable. Translations of mathematical monographs, vol. 26. AMS, Providence, Rhode Island (1969)Google Scholar
  4. 4.
    Israfilov, D.M.; Akgün, R.: Approximation in weighted Smirnov-Orlicz classes. J. Math. Kyoto Univ. 46(1), 755–770 (2006)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Israfilov, D.M.; Akgün, R.: Approximation by polynomials and rational functions in weighted rearrangement invariant spaces. J. Math. Anal. Appl. 346(2), 489–500 (2008)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Israfilov, D.M.; Testici, A.: Approximation in weighted Smirnov classes. Complex Var. Elliptic Equ. 60(1), 45–58 (2015)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Israfilov, D.M.; Testici, A.: Approximation in smirnov classes with variable exponent. Complex Var. Elliptic Equ. 60(9), 1243–1253 (2015)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Israfilov, D.M.; Testici, A.: pproximation by Faber-Laurent rational functions in Lebesgue spaces with variable exponent. Indag. Math. 27(4), 914–922 (2016)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Jafarov, S.Z.: On approximation of functions by p-Faber -Laurent rational functions. Complex Var. Elliptic Equ. 60(3), 416–428 (2005)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Jafarov, S.Z.: Approximation by rational functions in Smirnov-Orlicz classes. J. Math. Anal. Appl. 379(2), 870–877 (2011)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Kokilashvili, V.M.; Samko, S.G.: Weighted boundedness in Lebesgue spaces with variable exponents of classical operators on Carleson curves. Proc. A. Razmadze Math. Inst. 138, 106–110 (2005)MathSciNetMATHGoogle Scholar
  12. 12.
    Markushevich, A.: Theory of analytic functions, vol. 2. Izdatelstvo Nauka, Moscow (1968)MATHGoogle Scholar
  13. 13.
    Suetin, P.K.: Series of Faber polynomials. Gordon and Breach science publishers, Amsterdam (1998)MATHGoogle Scholar
  14. 14.
    Yurt, H.; Guven, A.: Approximation by Faber-Laurent rational functions on doubly connected domains. N. Z. J. Math. 44, 113–124 (2014)MathSciNetMATHGoogle Scholar
  15. 15.
    Warschawski, S.: Ber das ranverhalten der Ableitung derAbildunggsfunktion bei Konfermer Abbildung. Math. Z 35 (1932)Google Scholar

Copyright information

© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceTishreen UniversityLattakiaSyria

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